Analytic symmetries and the properties of phase trajectories (Q790632)

The author formulates a sufficient condition which guarantees the existence of an analytic normalizing transformation of a system \({\dot \rho}= R(\rho,\phi)\), \({\dot \phi}=\Omega(\rho,\phi)\), \(R(0,\phi)=0\) \(\rho,\phi\) are polar coordinates in the plane) in terms of analytic properties of the phase trajectories rather than in terms of those of \(R\) and \(\Omega\). Why such a condition should be of any interest remained a mystery to the present reviewer.